By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.

Exact solutions of the Hirota equation and vortex filaments motion

DEMONTIS, FRANCESCO;VAN DER MEE, CORNELIS VICTOR MARIA
2015

Abstract

By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.
Inverse Scattering Transform; Soliton solutions; Vortex filaments; Statistical and nonlinear physics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/134373
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